A polar motion prediction method considering periodic time-varying characteristics

Abstract

The application discloses a polar motion prediction method considering period time-varying characteristics, belongs to the technical field of space geodetic measurement, and is used for polar motion prediction and comprises the following steps: preparing a data set, constructing a polar motion complex time sequence, and determining optimal period parameters by using a differential evolution algorithm adaptive optimization; a complex domain harmonic model is constructed to calculate polar motion prediction values, and the fitting prediction values are extrapolated; an autoregressive model is constructed to calculate residual sequence prediction values; and the fitting prediction values and the residual sequence prediction values are added to obtain final polar motion prediction results. By introducing a differential evolution algorithm global optimization algorithm to adaptively determine time-varying period parameters in the polar motion sequence, more accurate fitting and prediction of key elements such as period, amplitude and phase change of Chandler wobble and annual term in the polar motion signal are realized, a more stable residual sequence is provided for the autoregressive model, and the accuracy and stability of polar motion prediction, especially medium and long term span prediction, are significantly improved as a whole.

Description

TECHNICAL FIELD

[0001] The application discloses a polar motion prediction method considering period time-varying characteristics and belongs to the technical field of space geodesy. BACKGROUND

[0002] Earth orientation parameters (EOP) are key parameters for the conversion between the celestial reference system and the earth reference system. The EOP includes nutation, precession, polar motion and length of day variation. Among them, polar motion refers to the change of the position of the earth rotation axis relative to the earth surface. High-precision EOP prediction is an important guarantee for the realization of spacecraft measurement and control, real-time satellite navigation, geodesy and other fields. Among them, due to complex excitation factors, high-precision polar motion prediction has always been a difficult problem in EOP prediction.

[0003] Existing researches show that polar motion mainly includes long trend items, Chandler items, annual items, seasonal items and high-frequency items. Among them, annual swing, Chandler swing and semi-annual swing are the most important components. The traditional polar motion prediction method is generally based on the combination of least squares (LS) and auto regression (AR) model (LS+AR model). The basic idea of this kind of method is: firstly, the deterministic trend items and fixed period items in the polar motion sequence are fitted and extrapolated by using the least squares model, and then the residual sequence after the least squares fitting is used to model and predict the random items by using the auto regression model.

[0004] However, the traditional least squares plus auto regression model has inherent limitations. A large number of studies have shown that the Chandler period and the annual period in the polar motion have significant time-varying characteristics, and the amplitude and period also have a large range of changes. The traditional model uses fixed period parameters, which cannot accurately track such time-varying characteristics, resulting in significant phase shift and error accumulation in medium and long-term prediction, thereby seriously restricting the further improvement of the prediction accuracy. SUMMARY

[0005] The purpose of the present application is to provide a polar motion prediction method considering period time-varying characteristics, so as to solve the problem of long-term prediction phase shift and error accumulation caused by the fact that the traditional least squares plus auto regression model cannot reflect the time-varying characteristics of Chandler swing and annual items due to the use of fixed period.

[0006] A polar motion prediction method considering period time-varying characteristics comprises:

[0007] S1. Prepare the dataset and construct a polar-shift complex time series. Within the preset period parameter boundary, randomly initialize the population of the differential evolution algorithm. Construct a fitted sequence model using the Chandler period and annual period parameters of the population individuals, and solve for the fitted values ​​of the population individuals. Using the differential evolution algorithm, determine the optimal combination of period parameters by maximizing the Pearson correlation coefficient between the fitted sequence and the polar-shift observed complex sequence. Determine the optimal individual in the polar-shift complex time series through adaptive optimization, and use the period parameters of the optimal individual as the optimal combination of period parameters.

[0008] S2. Construct a complex domain harmonic model based on the optimal combination of periodic parameters to calculate the polar motion prediction value. Perform least squares fitting on the polar motion complex time series to obtain the optimal complex domain harmonic model. Calculate the fitted prediction value based on the optimal complex domain harmonic model. Calculate the residual between the fitted prediction value and the observed polar motion value based on the time series to form a residual sequence.

[0009] S3. Construct an autoregressive model for the residual sequence, determine the optimal order and optimal autoregressive coefficients through the final prediction error criterion adaptive and least squares method, construct the optimal autoregressive model, and use the optimal autoregressive model to calculate the predicted value of the residual sequence.

[0010] S4. Add the fitted forecast value and the residual sequence forecast value to obtain the final polar motion forecast result.

[0011] S1 includes, S1.1, constructing a polar-shift complex time series, with the x-direction as the real part and the y-direction as the imaginary part:

[0012] ;

[0013] In the formula, For polar motion observation complex sequence, Let x be the polar motion component in the x-direction. Let be the polar motion component in the y-direction. The imaginary unit, For indexing time series, , This represents the total length of the time series.

[0014] S1 includes, and S1.2, randomly generating parameters within the boundaries of the set Chandler period parameter and annual period parameter, including... indivual The initial population of 2D real-valued vectors. The total number of individuals in the population. The total dimension of the parameters to be optimized is:

[0015] ;

[0016] ;

[0017] ;

[0018] In the formula, For parameters to be optimized, For indexing individuals in the population, Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. For in the interval A random number that is uniformly distributed within the range;

[0019] S1 includes S1.3, based on the population level. The Chandler cycles and annual cycles of each individual are used to construct the first... Fitted sequence model for each individual in the population:

[0020] ;

[0021] In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual;

[0022] The least squares method was used to fit the polar shift complex time series of the fitted sequence model to obtain the following results. , , and .

[0023] S1 includes S1.4, which uses the differential evolution algorithm to determine the optimal combination of periodic parameters by maximizing the Pearson correlation coefficient between the fitted sequence and the polar motion observation complex sequence. The Pearson correlation coefficient is:

[0024] ;

[0025] In the formula, The Pearson correlation coefficient is used. For the fitted sequence, For covariance, Standard deviation for standard deviation for standard deviation for The average value over a time series. for The average value over a time series; combinations of periodic parameters include Chandler periods and annual periods.

[0026] S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation:

[0027] ;

[0028] In the formula, For the mutation vector, This represents the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Distinguished random integers, and , , Neither pair is equal. , , For from the first Three distinct individuals randomly selected from the population;

[0029] S1 includes, S1.6, and... and Perform a binary crossover operation to generate experimental vectors. :

[0030] ;

[0031] In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes;

[0032] S1 includes S1.7, defining the fitness function. , To calculate the independent variable of the function based on steps S1.3 and S1.4 ,Will and Substitute them as the independent variables of the function. According to the greed principle, the better one is selected. Generation 1 The parameters to be optimized for each individual:

[0033] ;

[0034] S1 includes S1.8. Adaptive optimization includes repeating steps S1.3 to S1.7 until the maximum number of iterations is reached or the convergence condition is met, to obtain the optimal individual, and using the optimal individual as the optimal Chandler period and the optimal annual period.

[0035] S2 includes S2.1, which constructs a complex domain harmonic model based on the optimal Chandler period and the optimal annual period:

[0036] ;

[0037] In the formula, These are polar motion prediction values. For optimal Chandler cycles, Optimal annual cycle, The optimal six-month cycle is the best.

[0038] S2 includes S2.2, obtained by least-squares fitting of the polar-shift complex time series. , , and The optimal value, let for the optimal value of is the optimal value of is the optimal value of is the optimal value of , , and are substituted into the complex domain harmonic model to obtain an optimal complex domain harmonic model:

[0039] ;

[0040] In the formula, is the fitting prediction value, and is the optimal value of satisfies the sum of squares of the residuals between the polar motion observation values and the polar motion prediction values is minimum.

[0041] S2 includes S2.3, calculating the residuals between the polar motion observation values and the polar motion prediction values to form a residual sequence.

[0042] S3 includes S3.1, constructing an autoregressive model based on the residual sequence:

[0043] ;

[0044] In the formula, is a residual value, is the residual value at the moment, is a lag term, is a model order, is an index of the model order, , is an autoregressive coefficient, is the autoregressive coefficient of the order, is white noise, is the white noise at the moment.

[0045] S3 includes S3.2, determining by the final prediction error criterion adaptive and least square method, and the final prediction error criterion formula is:

[0046] ;

[0047] ;

[0048] In the formula, is the autoregressive model order, ​​​The final forecast error value at that time, For sample size, For order is The residual variance of the autoregressive model, To be optimal ,satisfy Minimum.

[0049] S3 includes, S3.3, and will Substitute the values ​​into the autoregressive model and calculate the corresponding autoregressive coefficients using the least squares method. ;

[0050] Will and corresponding Substituting into the autoregressive model, we obtain the optimal autoregressive model:

[0051] ;

[0052] In the formula, This represents the predicted value of the residual sequence.

[0053] S4 involves adding the fitted forecast values ​​and the residual sequence forecast values ​​to obtain the final polar motion forecast result:

[0054] ;

[0055] In the formula, This is the final polar motion forecast result.

[0056] Compared with existing technologies, the present invention has the following advantages: By introducing a differential evolution algorithm for global optimization, the present invention adaptively determines the time-varying periodic parameters in the polar shift sequence. This not only achieves more accurate fitting and prediction of key elements such as the changes in period, amplitude, and phase of the Chandler oscillation and annual term in the polar shift signal, but also provides a more stable residual sequence for the autoregressive model. Thus, the accuracy and stability of polar shift, especially the medium- and long-term span prediction, are significantly improved overall. Attached Figure Description

[0057] Figure 1 This is a flowchart of the technology of this invention;

[0058] Figure 2 This is a graph showing the variation of the mean absolute error of the polar motion x-direction component;

[0059] Figure 3 This is a graph showing the variation of the average absolute error of the polar motion y-direction component. Detailed Implementation

[0060] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application are clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0061] A polar motion prediction method considering periodic time-varying characteristics, comprising:

[0062] S1, preparing a data set, constructing a polar motion complex time series, randomly initializing a population of a differential evolution algorithm within a preset period parameter boundary, constructing a fitting sequence model with the Chandler period and annual period parameters of the population individuals, solving the fitting values of the population individuals, determining an optimal period parameter combination by maximizing the Pearson correlation coefficient of the fitting sequence and the polar motion observed complex sequence by using the differential evolution algorithm, determining the optimal individual in the polar motion complex time series by adaptive optimization, and taking the period parameters of the optimal individual as the optimal period parameter combination;

[0063] S2, constructing a complex domain harmonic model based on the optimal period parameter combination to calculate a polar motion prediction value, performing least square fitting on the polar motion complex time series to obtain an optimal complex domain harmonic model, calculating a fitting prediction value according to the optimal complex domain harmonic model, and constructing a residual sequence based on the residual between the fitting prediction value and the polar motion observed value calculated based on the time series;

[0064] S3, constructing an autoregressive model for the residual sequence, determining an optimal order and an optimal autoregressive coefficient by adaptive least square method according to a final prediction error criterion, constructing an optimal autoregressive model, and calculating a residual sequence prediction value by using the optimal autoregressive model;

[0065] S4, adding the fitting prediction value and the residual sequence prediction value to obtain a final polar motion prediction result.

[0066] S1 comprises S1.1, constructing a polar motion complex time series, taking the x direction as the real part and the y direction as the imaginary part:

[0067] ;

[0068] In the formula, is a polar motion observed complex sequence, is a component of the polar motion in the x direction, is a component of the polar motion in the y direction, is an imaginary unit, is an index of the time series, , is the total length of the time series;

[0069] S1 includes, and S1.2, randomly generating parameters within the boundaries of the set Chandler period parameter and annual period parameter, including... indivual The initial population of 2D real-valued vectors. The total number of individuals in the population. The total dimension of the parameters to be optimized is:

[0070] ;

[0071] ;

[0072] ;

[0073] In the formula, For parameters to be optimized, For indexing individuals in the population, Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. For in the interval A random number that is uniformly distributed within the range;

[0074] S1 includes S1.3, based on the population level. The Chandler cycles and annual cycles of each individual are used to construct the first... Fitted sequence model for each individual in the population:

[0075] ;

[0076] In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual;

[0077] The least squares method was used to fit the polar shift complex time series of the fitted sequence model to obtain the following results. , , and .

[0078] S1 includes S1.4, which uses the differential evolution algorithm to determine the optimal combination of periodic parameters by maximizing the Pearson correlation coefficient between the fitted sequence and the polar motion observation complex sequence. The Pearson correlation coefficient is:

[0079] ;

[0080] In the formula, The Pearson correlation coefficient is used. For the fitted sequence, For covariance, Standard deviation for standard deviation for standard deviation for The average value over a time series. for The average value over a time series; combinations of periodic parameters include Chandler periods and annual periods.

[0081] S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation:

[0082] ;

[0083] In the formula, For the mutation vector, This represents the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Distinguished random integers, and , , Neither pair is equal. , , For from the first Three distinct individuals randomly selected from the population;

[0084] S1 includes, S1.6, and... and Perform a binary crossover operation to generate experimental vectors. :

[0085] ;

[0086] In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes;

[0087] S1 includes S1.7, defining the fitness function. , To calculate the independent variable of the function based on steps S1.3 and S1.4 ,Will and Substitute them as the independent variables of the function. According to the greed principle, the better one is selected. Generation 1 The parameters to be optimized for each individual:

[0088] ;

[0089] S1 includes S1.8. Adaptive optimization includes repeating steps S1.3 to S1.7 until the maximum number of iterations is reached or the convergence condition is met, to obtain the optimal individual, and using the optimal individual as the optimal Chandler period and the optimal annual period.

[0090] S2 includes S2.1, which constructs a complex domain harmonic model based on the optimal Chandler period and the optimal annual period:

[0091] ;

[0092] In the formula, These are polar motion prediction values. For optimal Chandler cycles, Optimal annual cycle, The optimal six-month cycle is the best.

[0093] S2 includes S2.2, obtained by least-squares fitting of the polar-shift complex time series. , , and The optimal value, let for The optimal value, for The optimal value, for The optimal value, for The optimal value will , , and Substituting into the complex domain harmonic model yields the optimal complex domain harmonic model:

[0094] ;

[0095] In the formula, To fit the predicted value, The optimal value, satisfy The sum of squares of the residuals between the observations and the polar motion observations is minimized;

[0096] S2 includes, S2.3, based on calculate The residuals between the observations and the polar shift observations constitute a residual sequence.

[0097] S3 includes S3.1, constructing an autoregressive model based on residual sequences:

[0098] ;

[0099] In the formula, The residual value, for The residual value at time step, It is a lagged term. The model order is... For the index of the model order, , These are the autoregressive coefficients. For the first The autoregressive coefficient of order, It is white noise. for White noise at any given moment.

[0100] S3 comprises S3.2, determining by final pre-error criterion self-adaption and least square method The final pre-error criterion formula is:

[0101] ;

[0102] ;

[0103] In the formula, is the final pre-error value when the autoregressive model order is , n is the sample size, is the residual variance of the autoregressive model with order , and is the optimal , which satisfies minimum.

[0104] S3 comprises S3.3, substituting into the autoregressive model, and calculating the corresponding autoregressive coefficients by the least square method ;

[0105] Substituting and the corresponding into the autoregressive model, the optimal autoregressive model is obtained:

[0106] ;

[0107] In the formula, is the residual sequence pre-value.

[0108] S4 comprises adding the fitting pre-value and the residual sequence pre-value to obtain the final polar motion pre-result:

[0109] ;

[0110] In the formula, is the final polar motion pre-result.

[0111] Further description is made below with reference to the accompanying drawings. The technical flow of the present application is as follows: Figure 1 ​As shown, prepare polar motion data, input initial parameters, set the number of iterations, population initialization, construct a fitting sequence model, perform mutation operation on the initial population to obtain a mutation vector, perform crossover operation on the mutation vector to obtain an experimental vector, construct a fitness function, substitute the individual vector and the experimental vector into the fitness function as independent variables, then select the better individual, perform conditional judgment, if the stop condition is not met, return to the mutation operation, if the stop condition is met, output the optimal period parameter combination, including the optimal CW (Chandler period) and the optimal AW (annual period), use the obtained optimal period parameter combination (the optimal period parameter combination satisfies the highest correlation of the least square fitting data and the polar motion observation value) to construct an optimal complex domain harmonic model, fit the polar motion data, then divide into two branches, the first branch is an extrapolation prediction item based on the least square model, the second branch is a fitting residual item, then extrapolate through an AR (autoregressive) model to obtain a residual prediction value; finally, combine the results of the two branches to obtain a polar motion prediction value.

[0112] In order to intuitively illustrate the effectiveness of the present application, the EOP 20u23 C04 polar motion sequence published by the International Earth Rotation and Reference System Service (IERS) is taken as a data set, and the parameter setting conditions include: , , , , the maximum evolutionary iteration number is 100, the Chandler period is , and the annual period is .

[0113] The final polar motion prediction result obtained by the present application is compared with the Bulletin A published by the International Earth Rotation and Reference System Service (IERS) and the method of the present application. In the prediction experiment, the first prediction starting point is January 4, 2018, and then prediction is performed every 7 days, and the last prediction starting point is December 24, 2021, a prediction file with the same number of periods as Bulletin A is generated, a total of 208 periods. The basic data of each period is selected as the previous 10 years of the prediction time, and the prediction time length is 365 days. The present application selects the mean absolute error (MAE) to analyze and evaluate the prediction accuracy, and the calculation method of the MAE is:

[0114] ,

[0115] In the formula, is the absolute error of the period.

[0116] The prediction error result of the polar motion in the x direction is shown in Table 1:

[0117] Table 1, polar motion x-direction forecast error statistics table

[0118] ;

[0119] The polar motion y-direction forecast error results are shown in Table 2:

[0120] Table 2, polar motion y-direction forecast error statistics table

[0121] ;

[0122] Based on Table 1 and Table 2, in the short-term forecast of 1 to 10 days, the accuracy of the model of the application is comparable to that of the traditional least squares plus autoregressive model, and both are significantly better than Bulletin A (the highest improvement of 46.15% in the x-direction and 42.11% in the y-direction), which proves the effectiveness of the basic model framework; as the forecast span is extended, the advantage of the application begins to stand out. In the forecast span of 365 days, compared with Bulletin A, the prediction accuracy of the application in the x and y directions is improved by 37.27% and 25.32% respectively; compared with the traditional least squares plus autoregressive model, it is also improved by 14.88% and 13.14% respectively. This fully proves that the introduction of the differential evolution algorithm to optimize the periodic parameters effectively improves the long-term characterization ability of the model for the complex dynamic characteristics of the polar motion, and alleviates the problem of rapid decay of the accuracy of the traditional model in long-term prediction. Although the error of the application is slightly higher than that of Bulletin A in individual periods in the medium-term span, it is still generally better than the traditional least squares plus autoregressive model.

[0123] Figure 2 and Figure 3 respectively show the average absolute error of the four polar motion prediction schemes in the x and y directions. Among them, the LS+AR model, Bulletin A and the model of the application (DE+LS+AR) are represented by blue, red and green curves respectively. The small part of the figure is a local enlarged view of the prediction results of the first 30 days. From Figure 2 and 3It can be seen that, in the x direction and the y direction, compared with the fixed period LS+AR model, the three schemes of the model of the application have significant improvement in the prediction accuracy of medium and long term. In the x direction, compared with Bulletin A, the short-term (0-16 days) and long-term (135-365 days) prediction accuracy of the model of the application is obviously improved, which shows that the period parameters obtained by the method of the application provide a better model basis in the whole prediction period, so that the prediction trajectory is more reasonable, and thus the cumulative error is better controlled at the end of the longer prediction period. Therefore, the differential evolution algorithm combined with the least square and autoregressive model (DE+LS+AR) proposed in the application shows significant performance improvement in polar motion prediction, especially in the medium and long term prediction span, which reflects the advancement and reliability of the method.

[0124] In summary, the application takes into account the time-varying nature of the polar motion annual period and the Chandler period, first applies the differential evolution algorithm to the optimization of the polar motion period parameter, optimizes the polar motion period parameter according to the historical data, not only realizes more accurate fitting and prediction of the key elements such as period, amplitude and phase change of the Chandler swing and annual term in the polar motion signal, but also provides a more stable residual sequence for the autoregressive model, thereby significantly improving the accuracy and stability of the polar motion, especially the medium and long term prediction span.

[0125] The above embodiments are only used to illustrate the technical solutions of the application, rather than limit them. Although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.

Claims

1. A polar motion prediction method taking into account periodic time-varying characteristics, characterized in that, Comprise: S1, prepare data set, construct polar motion complex time series, randomly initialize the population of differential evolution algorithm within the preset period parameter boundary, construct the fitting sequence model with the Chandler period and annual period parameters of the population individuals, and solve the fitting values of the population individuals, determine the optimal period parameter combination by maximizing the Pearson correlation coefficient between the fitting sequence and the polar motion observed complex sequence by using the differential evolution algorithm, determine the optimal individual in the polar motion complex time series by adaptive optimization, and take the period parameters of the optimal individual as the optimal period parameter combination; S2, based on the optimal period parameter combination, construct a complex domain harmonic model to calculate the polar motion prediction value, obtain the optimal complex domain harmonic model by least square fitting of the polar motion complex time series, calculate the fitting prediction value according to the optimal complex domain harmonic model, and construct a residual sequence based on the residual between the time series fitting prediction value and the polar motion observed value; S3, construct an autoregressive model for the residual sequence, determine the optimal order and optimal autoregressive coefficient by the final prediction error criterion adaptive and least square method, construct the optimal autoregressive model, and calculate the residual sequence prediction value by using the optimal autoregressive model; S4, add the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result; S1 includes, S1.1, construct the polar motion complex time series, taking the x direction as the real part and the y direction as the imaginary part: ； wherein is a complex sequence of polar motion observations, is a component of polar motion in the x-direction, is a component of polar motion in the y-direction, is the imaginary unit, is an index of the time series, , is the total length of the time series; S1 comprises, S1.2, within the boundaries of the set chandler period parameter and the annual period parameter, randomly generating an initial population of individuals of two-dimensional vectors of real values, wherein N is the total number of population individuals, wherein D is the total dimensionality of the parameters to be optimized, the parameters to be optimized being: ； ； ； In the formula, For parameters to be optimized, For indexing individuals in the population, Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. For in the interval A random number that is uniformly distributed within the range; S1 comprises, S1.3, constructing a fitted sequence model for the population individuals based on the Chandler period and the annual period of the population individuals S1.3.1, constructing a fitted sequence model for the population individuals based on the Chandler period of the population individuals​ ； In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual; The least square method is used to fit the polar motion complex time series with the fitted sequence model, and the following are obtained , , and ; S1 includes, S1.4, use the differential evolution algorithm to maximize the Pearson correlation coefficient between the fitting sequence and the polar motion observed complex sequence to determine the optimal period parameter combination, and the Pearson correlation coefficient is: ； wherein is the Pearson correlation coefficient, is the fitted sequence, is the covariance, is the standard deviation, is the standard deviation of is the standard deviation of is the average over the time series, is the average over the time series; the combination of periodic parameters comprises the Chandler period and the annual period; S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation: ； In the formula, For the mutation vector, This represents the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Distinguished random integers, and , , Neither pair is equal. , , For from the first Three distinct individuals randomly selected from the population; S1 comprises, S1.6, performing a binary cross operation on and the experimental vectors : ； In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes; S1 includes S1.7, defining the fitness function. , To calculate the independent variable of the function based on steps S1.3 and S1.4 ,Will and Substitute them as the independent variables of the function. According to the greed principle, the better one is selected. Generation 1 The parameters to be optimized for each individual: ； S1 includes, S1.8, adaptive optimization includes, repeat steps S1.3 to S1.7 until the maximum iteration number is reached or the convergence condition is met, obtain the optimal individual, and take the optimal individual as the optimal Chandler period and the optimal annual period.

2. The polar motion prediction method of claim 1, wherein, S2 includes, S2.1, based on the optimal Chandler period and the optimal annual period, construct a complex domain harmonic model: ； wherein is the polar motion prediction value, is the optimal Chandler period, is the optimal annual period, is the optimal semiannual period.

3. The polar motion prediction method of claim 2, wherein, S2 comprises, S2.2, performing least square fitting on the polar motion complex time series to obtain the optimal values of , , and , let be the optimal value of , be the optimal value of , be the optimal value of , be the optimal value of , substitute , , and into the complex domain harmonic model to obtain the optimal complex domain harmonic model: ； wherein is the optimal value of is the optimal value of satisfies the sum of squares of the residuals between the polar motion observations and the predicted values is minimized. S2 comprises, S2.3, based on calculating the residuals between the polar motion observations and the calculated polar motion values, constituting a residual series.

4. The polar motion prediction method of claim 3, wherein, S3 includes, S3.1, based on the residual sequence, construct an autoregressive model: ； In the formula, The residual value, for The residual value at time step, It is a lagged term. The model order is... For the index of the model order, , These are the autoregressive coefficients. For the first The autoregressive coefficient of order, It is white noise. for White noise at any given moment.

5. The polar motion prediction method of claim 4, wherein, S3 comprises, S3.2, determining by a final pre-error criterion adaptation and least square method The final pre-error criterion formula is: ； ； wherein is the final prediction error value when the autoregressive model order is , is the sample size, is the residual variance of the autoregressive model of order , is the optimal satisfying is minimal.

6. The polar motion prediction method of claim 5, wherein, S3 comprises, S3.3, determining Substitute into the autoregressive model, using the least squares method to calculate the corresponding autoregressive coefficients ; The and the corresponding substituted into the autoregressive model, the optimal autoregressive model is obtained: ； In the formula, is the prediction value of the residual sequence.

7. The polar motion prediction method of claim 6, wherein, S4 includes, add the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result: ； In the formula, is the final polar motion prediction result.

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